Massachusetts Institute of Technology Handout ?? 6.042J/18.062J: Mathematics for Computer Science September 29, 1998 Professors Nancy Lynch and Srinivas Devadas

The Aymptotic Cheat Sheet

1 Notation

Asymptotic notation consists of six funny symbols used to describe relative growth rate of functions. These symbols are defined in the table below.

f(n) = O(g(n)) f grows no faster than g Frequently used to give an upper bound on the running time or memory requirement of a program.

“True, your algorithm has run time O(n log n), and my algorithm is only O(n^{2}), but because I’m a hacker and you are a theoretician, my program still runs faster for n < 1000000.”

These exists an n_{0} and a constant c > 0 such that for all n ≥ n_{0}, f(n) ≤ cg(n).